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I wonder if "iff" is considered a real word (as LEO says) or is it just an abbreviation (as in Wiktionary)?

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Does this have anything to do with today's XKCD? – yoozer8 Mar 23 '12 at 7:47
@Jim Yes. You got me. – MBober Mar 23 '12 at 7:51
It’s considered an abomination. [If you find that writing “if and only if” is too long, use the proper symbol, i.e. “↔”] – Konrad Rudolph Mar 23 '12 at 11:12
@Konrad: For those writing metalogical statements, "↔", "⇔", and "iff" work at different levels and all three are needed. "A ↔ B ⇔ ((A ∧ B) ∨ ~(A ∨ B)) iff our definitions follow standard propositional semantics." ↔ is used as a truth function, ⇔ is used as equivalence, and iff is used to explain the conditions when the equivalence holds. – user2400 Mar 23 '12 at 12:28
@Konrad, specifically who considers it an abomination? That's a strong statement, and I think there are many, many people who would disagree. Are you referring specifically to usage outside of mathematics? – amcnabb Mar 23 '12 at 16:14
up vote 21 down vote accepted

I would count it as jargon and I'd never use it in prose. It's a programming/maths term meaning if and only if and should be restricted to circles where it's likely to be understood (edit like XKCD ).

The question of whether it's an abbreviation is interesting. It's obviously shorter than "if and only if" but I think I'd say it was a more of a symbol. Perhaps that's my programming background coming out [where symbol has a particular meaning (see number 2 here)]. However as it consists of more than one recognisable letter, it might be better to say it's an abbreviation

Here's an Ngram which shows that iff has become more popular recently, corresponding to the increase in computing. That may explain the increase in "if and only if" as well. I have no idea whether the incidence around 1800 is simply an alternative spelling of if or whether that actually meant "if and only if".

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It is not (only) a programming term, however. More of a logic term, I would say. – Eyvind Mar 23 '12 at 8:26
You're right, as today's XKCD indicates. But I'm not an expert in formal logic. And not an expert programmer either(!) but that's where my experience lies. – Andrew Leach Mar 23 '12 at 8:33
@Eyvind More a maths and logic term. Often used in mathematical proofs (often the proof is to prove the "iff" in a statement). – Richard Mar 23 '12 at 11:44
Philosophy, math, CS, ling, engin, they all use it. But never in speech. There is no special pronunciation difference between iff and if, so it couldn't be used in speech. It's strictly in informal writing (handouts, blackboard, notes, blogs, letters, etc.) – John Lawler Mar 23 '12 at 17:15
@JohnLawler Actually there is an important (critical) distinction in how if and iff are pronounced: if is pronounced "if", and iff is pronounced "if and only if" - In the context of formal logic they have substantially different meanings. iff is a generally accepted abbreviation in the Mathematics and Computer Science fields (and probably others that invoke formal logic), but it is definitely an abbreviation/shorthand, not a word. – voretaq7 Mar 23 '12 at 18:40

While acknowledging the excellent answer from @Andrew Leach, one man's jargon is another man's specialized terminology. To the non-mathematician, this is jargon. To the logician, this is an abbreviation that is used in a similar way (though not as frequently) as QED. (At the bottom of a proof, a mathematician will write QED, standing for quod erat demonstrandum, to indicate that he or she has proven that which was set out to be proven.) You may find QED in popular usage, but it is both specialized terminology and an abbreviation.

I first ran across IFF in my 8th grade algebra class, and it was used in logic truth tables. It meant, as others have correctly stated, "If-and-only-if."

In the context of the XKCD comic, it means Honk if (and only if) you love formal logic. The truth table would be:

You love              You honk           You obey the 
formal logic                             bumper sticker
Yes                   Yes                Yes
No                    No                 Yes
Yes                   No                 No
No                    Yes                No

This means that if you honk because the driver swerved into your lane, then you are not obeying the bumper sticker (or the truth value of the bumper sticker's logical statement). And if you don't honk even though you love formal logic, then you're not obeying the truth value of the bumper sticker.

My experience in both programming and math has seen IFF rarely in programming and sometimes in math and logic. Few programmers, for instance, would recognize the equivalence between ~ XOR (not Exclusive OR operation) and IFF.

Q.E.D., but IFF you understood the truth table.

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+1 This is a great explanation of iff, although it's not good driving advice at all. – J.R. Mar 23 '12 at 14:25
Also, writing Q.E.D. at the end of proofs is a bit unfashionable these days. The current fashion is to draw a little black box, sometimes called a 'tombstone'. – Simon Nickerson Mar 23 '12 at 16:58
My profs would sometimes use the "Therefore" sign (U+2234 or ∴) at a conclusion, and in place of QED; this was more for lemmas than proofs. I will not dispute "unfashionable." My exposure to QED and IFF were back in the day when "high tech" meant a K&E slide rule or a four-function calculator. – rajah9 Mar 23 '12 at 17:32

OED 1971 doesn't list iff at all. The American Heritage Dictionary of the English Language, Fourth Edition says it's an abbreviation. Difficult to consider it a real word when it's normally pronounced as three separate letters.

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Oh, and the New Zealand Oxford Dictionary (2005) lists iff, but doesn't label it as an abbreviation. In my opinion, it's wrong not to do so. – user16269 Mar 23 '12 at 8:02
The online version of the OED has it and defines it as "A written form of abbreviation of the phrase ‘if and only if’, always read as ‘if and only if’, used in Math. and Logic to introduce a condition that is necessary as well as sufficient, or a statement that is implied by and implies the preceding one.'" – Barrie England Mar 23 '12 at 8:08
It's normally pronounced as for different words. – Hugo Mar 23 '12 at 8:25
Fair enough then. When I studied logic, the lecturers always said "if and only if". They only said "I. F. F." when introducing the notation for the first time. – Hugo Mar 23 '12 at 8:33
@David: in my experience, this abbreviation is pronounced "if and only if" in the same way etc is pronounced "et cetera". That in your experience it's pronounced "I F F" is interesting, but doesn't make one more valid than the other. – TimLymington Mar 23 '12 at 9:43

Re: is iff a word, or an abbreviation?

Does it need to be one or the other? It doesn't seem to be either one, in a pure sense.

I'm more comfortable identifying it as shorthand for "if and only if".

Dictionaries specifically relate the word shorthand to the standardized system of stenography, but many also list a secondary definition, something along the lines of "an abbreviated or shortened way of communicating something."

Wear the shoe iff it fits... In this case, I think shorthand fits better than either abbreviation or word.

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Personally, I don't really care if it's listed or not.

IFF is, as far as I know, an established contraction of if and only if in engineering, physics, philosophy (I believe the first experience I had with IFF was when our philosophy professor used it), and as I recall in mathematics as well. Some people are snarky about it, some aren't. I use it all the time. I've seen it used in all the areas above over the past three or four decades.

Perhaps not definitively a "word" in the spoken sense. but a "working" word or defacto written word? Yes, pretty much.

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